The safer option is both. Obviously.

But here's how I would think about the question. I consider the tarp to be more versatile for protection from wet circumstances, such as rain or wet snow, while the bivy probably is best at maintaining a warm air envelope around you and keeping body heat in, at least if the weather is dry. Once wetness invades your bivy its effectiveness is much reduced. So, I'd favor the tarp if it is wet and bivy when its dry.